Improved Hartree-Fock resummations and spontaneous symmetry breaking

Abstract

The standard Hartree-Fock approximation of the $O(N)$-invariant ${\ensuremath{\phi}}^{4}$ model suffers from serious renormalization problems. In addition, when the symmetry is spontaneously broken, another shortcoming appears in relation to the Goldstone bosons: they fail to be massless in the intermediate states. In this work, within the framework of out-of-equilibrium Quantum Field Theory, we propose a class of systematic improvements of the Hartree-Fock resummation which overcomes all the above mentioned difficulties while ensuring also exact Renormalization-Group invariance to one loop.